Add The Following Polynomials:$\[ \begin{array}{r} 6x^2 - 5x + 3 \\ +\quad 3x^2 + 7x - 8 \\ \hline \end{array} \\]Choose The Correct Result:A. \[$9x^2 + 2x + 11\$\]B. \[$9x^2 - 2x + 5\$\]C. \[$9x^2 + 12x - 5\$\]D.
Introduction
Polynomials are algebraic expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. In this article, we will focus on adding polynomials, which is an essential operation in algebra. We will use the given example to demonstrate the process of adding polynomials and provide a step-by-step guide on how to do it.
What are Polynomials?
A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The variables in a polynomial are usually represented by letters such as x, y, or z, and the coefficients are numbers that are multiplied with the variables. For example, 2x + 3y - 4 is a polynomial.
Adding Polynomials: A Step-by-Step Guide
To add polynomials, we need to follow a step-by-step process. Here's how to do it:
Step 1: Identify the Like Terms
Like terms are terms that have the same variable and exponent. In the given example, we have two polynomials:
{ \begin{array}{r} 6x^2 - 5x + 3 \\ +\quad 3x^2 + 7x - 8 \\ \hline \end{array} \}
We need to identify the like terms in both polynomials. The like terms in this example are:
- and
- and
- and
Step 2: Add the Like Terms
Now that we have identified the like terms, we can add them together. We add the coefficients of the like terms and keep the variable and exponent the same.
Step 3: Write the Result
Now that we have added the like terms, we can write the result. The result of adding the two polynomials is:
Conclusion
Adding polynomials is an essential operation in algebra. By following the step-by-step guide outlined in this article, you can add polynomials with ease. Remember to identify the like terms, add them together, and write the result. With practice, you will become proficient in adding polynomials and be able to solve more complex algebraic problems.
Answer
The correct result of adding the two polynomials is:
This is option B.
Discussion
Adding polynomials is a fundamental operation in algebra. It is used to simplify expressions and solve equations. In this article, we have demonstrated the process of adding polynomials and provided a step-by-step guide on how to do it. We have also discussed the importance of identifying like terms and adding them together.
Common Mistakes
When adding polynomials, there are several common mistakes that students make. These include:
- Failing to identify like terms
- Adding unlike terms together
- Forgetting to add the coefficients of like terms
- Writing the result incorrectly
To avoid these mistakes, it is essential to follow the step-by-step guide outlined in this article and practice adding polynomials regularly.
Practice Problems
To practice adding polynomials, try the following problems:
- Add the polynomials: and
- Add the polynomials: and
- Add the polynomials: and
Conclusion
Introduction
In our previous article, we discussed the process of adding polynomials and provided a step-by-step guide on how to do it. In this article, we will answer some frequently asked questions about adding polynomials.
Q: What are like terms?
A: Like terms are terms that have the same variable and exponent. For example, and are like terms because they both have the variable and the exponent .
Q: How do I identify like terms?
A: To identify like terms, you need to look for terms that have the same variable and exponent. For example, in the polynomial , the like terms are and because they both have the variable .
Q: What happens when I add like terms?
A: When you add like terms, you add the coefficients of the like terms and keep the variable and exponent the same. For example, .
Q: Can I add unlike terms?
A: No, you cannot add unlike terms. Unlike terms are terms that have different variables or exponents. For example, and are unlike terms because they have different variables.
Q: What is the result of adding two polynomials?
A: The result of adding two polynomials is a new polynomial that is the sum of the two original polynomials. For example, if you add the polynomials and , the result is .
Q: How do I write the result of adding two polynomials?
A: To write the result of adding two polynomials, you need to combine the like terms and write the result in the form of a polynomial. For example, if you add the polynomials and , the result is .
Q: What are some common mistakes to avoid when adding polynomials?
A: Some common mistakes to avoid when adding polynomials include:
- Failing to identify like terms
- Adding unlike terms together
- Forgetting to add the coefficients of like terms
- Writing the result incorrectly
Q: How can I practice adding polynomials?
A: You can practice adding polynomials by working through examples and exercises. You can also use online resources and practice tests to help you improve your skills.
Q: What are some real-world applications of adding polynomials?
A: Adding polynomials has many real-world applications, including:
- Simplifying algebraic expressions
- Solving equations
- Modeling real-world situations
- Calculating areas and volumes of shapes
Conclusion
Adding polynomials is an essential operation in algebra. By following the step-by-step guide outlined in our previous article and answering the frequently asked questions in this article, you can become proficient in adding polynomials and be able to solve more complex algebraic problems.
Practice Problems
To practice adding polynomials, try the following problems:
- Add the polynomials: and
- Add the polynomials: and
- Add the polynomials: and